Theorems · Definition · field theory

InfiniteGalois.continuousMulEquivToLimit

(k : Type u_3) →
  (K : Type u_4) →
    [inst : Field k] →
      [inst_1 : Field K] →
        [inst_2 : Algebra k K] →
          [IsGalois k K] →
            Gal(K/k) ≃ₜ* ↑(ProfiniteGrp.limit (InfiniteGalois.asProfiniteGaloisGroupFunctor k K)).toProfinite.toTop

The ContinuousMulEquiv between Gal(K/k) and lim Gal(L/k) where L is a FiniteGaloisIntermediateField ordered by inverse inclusion, obtained from InfiniteGalois.mulEquivToLimit

Defined in: Mathlib.FieldTheory.Galois.Profinite
Cited by: 0 results in Mathlib
Foundations: Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra IsGalois

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Functor.objstatement · cited by 19,642
Algebrastatement and proof · cited by 11,388
Oppositestatement · cited by 8,081
Fieldstatement and proof · cited by 7,404
Subgroupstatement · cited by 3,593
TopCat.carrierstatement and proof · cited by 3,184
TopCatstatement · cited by 1,889
AlgEquivstatement and proof · cited by 1,681
MulEquivproof · cited by 1,142
TotallyDisconnectedSpacestatement · cited by 295
CompHausLike.toTopstatement and proof · cited by 258
IsGaloisstatement and proof · cited by 149

Cited by1

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InfiniteGalois.profiniteGalGrpIsoLimitproof · cited by 0